Scale a Vector
Double a Vector.
Vector has magnitude and direction.
Double Vector
Triple Vector
Copy vector AB to point A_1
Vector has magnitude and direction
Add Vector AB to Vector CD
Use the Parallelogram Law
Question 4.3.1
Using a compass and straightedge, describe how you would construct the fourth vertex of the parallelogram given AB and CD placed at the same starting point.
Question 4.3.2
Prove that AB + CD = CD + AB using the Parallelogram Law.
Def. - Closed Under Addition
A set is closed under addition if adding any two vectors from the set always produces another vector that is also in the set.
For example, if you add two vectors, the result is always a vector (not a scalar or something else). Vector addition always produces a vector, so we say vectors are closed under addition.
Question 4.3.3
Explain why your proof of AB + CD = CD + AB also shows that vectors are closed under addition.